Simulations of the Dynamics Generated

in the Solar Atmosphere by Solar Global

Oscillating Eigenmodes

Michael Griffiths, Viktor Fedun, Robertus Erdélyi

The Solar Wave Theory Group

And Corporate Information and Computing Services

The University of Sheffield

National Astronomy MeetingUniversity of Portsmouth

June 2014

Outline

• Solar Global Oscillating Eigenmodes

• A model for studying dynamics in the atmosphere

• Simulation

• Evidence of induced Dynamics

• Conclusion and Future Work

Dynamics in the Solar Atmosphere

• Earliest observations of motions of the solar surface around 1918, (St.John C.E. et al, from Doppler Shift when studying solar rotation).

• Leighton1960, Vertical motions 300-400m/s,explained by Ulrich1970

• The solar p modes are generated by global resonant oscillations and turbulent motions just beneath the photosphere.

• Modes trapped below the photosphere refracted by sharp change in density

• Power peak at 5 – minutes p mode oscillations

l=4,m=2 l=10,m=4 l=20,m=2

Solar Global Eigen modes

of Oscillation Hydrodynamic Waves Gravitating Slab

Quantization condition – l usually large

Spherical solution using spherical harmonics

• Demonstrate code validity by repeating earlier

hydrodynamic 2D models of Malins and Erdelyi

• Demonstrate cavity modes in the

Chromosphere

• Surface modes in the transition region

• Understand dynamics allowing mode tunnelling

and energy leakage into the corona

• Modes evanescent around photosphere – inhibit

propagation into corona

• Upper and lower turning points determined by

order

Objectives

Vertical driver to Induce

Dynamics in the

Solar Atmosphere • Represent oscillation modes as a vibrating membrane

• Driver located at temperature minimum

• Deliver same amount of energy for different modes

• Fully stratified quiet solar

atmosphere based on VALIIIC

and McWhirter

• Model of the stratified solar

atmosphere

• Height upto 6Mm

• Cross section 4Mmx4Mm

• 128x128x128 computational

domain

• Local acoustic cut-off

• Propagation below cutoff

• Evanescence (above cutt-

off)

• Cutoff calculated in different ways

• Isothermal atmosphere

• Highly stratified

• Models with 30s,180s,300s

drivers

• 00,01 and 02 modes

• Run normal mode fixed energy

Computational Model

Stratified MagnetohydrodynamicsAcceleratedUsing GPUs:SMAUG

• SMAUG is a novel fully non-linear MHD code based on SAC/VAC (Shelyag et al 2008)

• designed for simulations of linear and non-linear wave propagation

• with gravitationally strongly stratified magnetised plasma.

• Version of SAC ported to GPU(Graphical Processing Units)

• Single GPU

• 2.5xfaster than latest Intel Xeon (using 8 cores)

• Multiple GPU version available

Validation of SMAUG(Flux Tube with Torsional Driver)

128x128x128

1.5x2x2Mm

Fully

stratified

quiet solar

atmosphere

based on

VALIIIC

Flux tube

1000G

Driver

Amplitude

200km/s

Period

Also Orszag-

Tang, Brio-

Wu and

explosion

modelFedun et Al., Astrophys. J. Lett 740:L46,2011 movie

Energy leakage and Evolution• For each time step integrate the total

energy over the model cross section

• Plot the energies for the transition

region and into the Corona

• 180s and 300s modes provide

energy leakage with period the

same as that of the driver

• 30s driver is the least efficient at

coronal energy leakage.

• Evidence for non linear beahviour

Variation of Energy leakage

with Driver frequency• Integrate perturbed energy over cross sectional and over either the

transition region or the corona

• Take average over the simulation time

• For the 02 mode 180s driver dominates

Variation of Energy leakage

with Driver frequency

Compute time averaged perturbation energy for the 00 and 01 modes

• fundamental mode 5 min driver (300s) effective for energy supply to the corona

region and 3 min driver effective for TR

• 01 mode 5 min nothing for corona and 3 min again effective for TR

• 02 mode 5 min nothing for corona and 3 min effective for corona

Distance Time Plots For 0,1 mode from left to right 30s, 180s, 300s for the vertical component of

the velocity

Driver is 0,1 Mode with Period 300s

(z Component of Velocity)

• Mainly future work!

• GPU code performs well

• Results provide evidence for energy leakage into the corona

• fundamental mode 5 min driver (300s) effective for energy supply to the

corona region and 3 min driver effective for TR

• 01 mode 5 min nothing for corona and 3 min again effective for TR

• 02 mode 5 min nothing for corona and 3 min effective for corona

• Distance time plots illustrate cavity modes in the chromosphere

• For 300s and 180s drivers clear indication of induced dynamics in the corona

• Unexplained resonances e.g. for 30s driver probably resulting from non-linear

behaviour

• Further characterisation of the normal modes and run models with a greater

range of modes of oscillation

• Genuine MHD examples

• Vertical B field

• Horizontal B field

• Flux tubes

Conclusion and Future Work

• Thank you for Listening

• http://uk.virginmoneygiving.com/mikeg64

Driver is 0,1 Mode with Period 30s

Driver is 0,1 Mode with Period 180s